I am an undergraduate freshman and I go to a semi-target university. I am trying to decide between a statistics and an applied math major. Unfortunately, I'm already behind in either curriculum so I don't have time to experiment each major.
I know that people say major doesn't matter that much as long as it's quantitative; however, I am really just wondering which of these majors has the best curriculum, and hence will prepare me best for a mfe and a job in quantitative finance?
Statistics:
-Calc 1,2,3
-Intro to Stats
-Intro to programming
-Intro to decision science - Introduction to basic concepts and techniques of decision-making and information management in business, economics, social and physical science. Topics include discrete optimization, discrete probability, networks, decision trees, games, Markov chains
-Deterministic Models in Operations Research - Linear, integer, nonlinear and dynamic programming, classical optimization problems, network theory
-Introduction to probability - Probability models for random experiments. Basic properties of probability measures. Conditional probability and independence. Discrete random variables: hypergeometric, binomial, geometric, negative binomial, and Poisson. Continuous random variables: uniform, exponential, Gaussian, Cauchy and gamma. Jointly distributed random variables. Definition and basic properties of expectations, variances, covariances and correlations. Basic inequalities for probabilities and expectations. Laws of large numbers and the central limit theorem
-Stochastic Models in Operation Research - Introduction to Markov chains, Poisson process, continuous-time Markov chains, renewal theory. Applications to queueing systems inventory, and reliability, with emphasis on systems modeling, design, and control
-Statistical methods I - The topics include simple and multiple linear regression, matrix representation of the regression model, statistical inferences for regression model, diagnostics and remedies for multicollinearity, outlier and influential cases, polynomial regression and interaction regression models, model selection, weighted least square procedure for unequal error variances, and ANOVA model and test. Statistical software SAS will be used throughout the course to demonstrate how to apply the techniques on real data.
-Statistical methods II - The focus of this course is on analysis of time series data, that is, data recorded in time. The topics of the course include estimation and elimination of trend and seasonal components, stationary time series, ARMA models, spectral analysis, modeling and forecasting of time series. Some statistical software will be used throughout the course to demonstrate how to apply the techniques on real time series data
-Linear Algebra for Applications - Algebra of matrices with applications. Solution of linear systems by Gaussian elimination. The Gram-Schmidt procedure. Eigenvalues and eigenvectors.
Statistics Electives:
Computational Mathematics for Decision Sciences - Reviews basic mathematical and computational theory required for analyzing models that arise in operations research, management science, and other policy sciences. Solution techniques that integrate existing software into student-written computer programs will be emphasized
Mathematical Statistics - Derivation and analysis of point estimators using decision theory, including the methods of Bayes and minimax estimation, maximum likelihood, method of moments, and unbiased estimation. Confidence intervals. Hypothesis testing, including Bayesian methods, multiple hypotheses, the Neyman-Pearson Lemma, simple and composite hypotheses, likelihood ratio tests, Type I and Type II errors, power calculations. Uses of and relationships between the families of standard probability models, including the Normal, Gamma, Chi-Squared, Student's T, Uniform, Beta, Binomial, Negative Binomial, Poisson, Hypergeometric, and Cauchy distributions, as well as the Poisson Process and the Bernoulli Process
Introduction to numerical analysis - Iterative methods, interpolation, polynomial and spline approximations. Numerical differentiation and integration, solution of ODEs and PDEs.
Applied Math
-Calc 1,2,3
-Intro to programming
-Discrete Mathematics
-Linear Algebra and Differential equations
-Advanced Calculus 1 :
Real number system.
Continuity, uniform continuity, and differentiability of functions of one variable.
The Riemann integral in one variable.
Uniform convergence, infinite series, power series.
-Linear Algebra or Linear Algebra for applications
-Introduction to numerical analysis
Iterative methods, interpolation, polynomial and spline approximations.
Numerical differentiation and integration, solution of ODEs and PDEs.
-Computer Assisted Mathematical Problem Solving
Computer as a tool in solving a variety of mathematical problems.
Possible topics: roots of equations, solutions to differential equations, others.
Introduction to appropriate programming language. Emphasis on graphics.
-Mathematical Modeling
Models and numerical simulations, using differential equations, iterated maps, and probability.
These are most likely the classes I will be taking if I decide to do either a stats or applied math major. I will probably take a couple of programming classes as well.
Also, I plan on double majoring in finance (since my university has a very good b-school)
So.... based on the classes I provided, which would be a better route? Stats or applied math?
I know that people say major doesn't matter that much as long as it's quantitative; however, I am really just wondering which of these majors has the best curriculum, and hence will prepare me best for a mfe and a job in quantitative finance?
Statistics:
-Calc 1,2,3
-Intro to Stats
-Intro to programming
-Intro to decision science - Introduction to basic concepts and techniques of decision-making and information management in business, economics, social and physical science. Topics include discrete optimization, discrete probability, networks, decision trees, games, Markov chains
-Deterministic Models in Operations Research - Linear, integer, nonlinear and dynamic programming, classical optimization problems, network theory
-Introduction to probability - Probability models for random experiments. Basic properties of probability measures. Conditional probability and independence. Discrete random variables: hypergeometric, binomial, geometric, negative binomial, and Poisson. Continuous random variables: uniform, exponential, Gaussian, Cauchy and gamma. Jointly distributed random variables. Definition and basic properties of expectations, variances, covariances and correlations. Basic inequalities for probabilities and expectations. Laws of large numbers and the central limit theorem
-Stochastic Models in Operation Research - Introduction to Markov chains, Poisson process, continuous-time Markov chains, renewal theory. Applications to queueing systems inventory, and reliability, with emphasis on systems modeling, design, and control
-Statistical methods I - The topics include simple and multiple linear regression, matrix representation of the regression model, statistical inferences for regression model, diagnostics and remedies for multicollinearity, outlier and influential cases, polynomial regression and interaction regression models, model selection, weighted least square procedure for unequal error variances, and ANOVA model and test. Statistical software SAS will be used throughout the course to demonstrate how to apply the techniques on real data.
-Statistical methods II - The focus of this course is on analysis of time series data, that is, data recorded in time. The topics of the course include estimation and elimination of trend and seasonal components, stationary time series, ARMA models, spectral analysis, modeling and forecasting of time series. Some statistical software will be used throughout the course to demonstrate how to apply the techniques on real time series data
-Linear Algebra for Applications - Algebra of matrices with applications. Solution of linear systems by Gaussian elimination. The Gram-Schmidt procedure. Eigenvalues and eigenvectors.
Statistics Electives:
Computational Mathematics for Decision Sciences - Reviews basic mathematical and computational theory required for analyzing models that arise in operations research, management science, and other policy sciences. Solution techniques that integrate existing software into student-written computer programs will be emphasized
Mathematical Statistics - Derivation and analysis of point estimators using decision theory, including the methods of Bayes and minimax estimation, maximum likelihood, method of moments, and unbiased estimation. Confidence intervals. Hypothesis testing, including Bayesian methods, multiple hypotheses, the Neyman-Pearson Lemma, simple and composite hypotheses, likelihood ratio tests, Type I and Type II errors, power calculations. Uses of and relationships between the families of standard probability models, including the Normal, Gamma, Chi-Squared, Student's T, Uniform, Beta, Binomial, Negative Binomial, Poisson, Hypergeometric, and Cauchy distributions, as well as the Poisson Process and the Bernoulli Process
Introduction to numerical analysis - Iterative methods, interpolation, polynomial and spline approximations. Numerical differentiation and integration, solution of ODEs and PDEs.
Applied Math
-Calc 1,2,3
-Intro to programming
-Discrete Mathematics
-Linear Algebra and Differential equations
-Advanced Calculus 1 :
Real number system.
Continuity, uniform continuity, and differentiability of functions of one variable.
The Riemann integral in one variable.
Uniform convergence, infinite series, power series.
-Linear Algebra or Linear Algebra for applications
-Introduction to numerical analysis
Iterative methods, interpolation, polynomial and spline approximations.
Numerical differentiation and integration, solution of ODEs and PDEs.
-Computer Assisted Mathematical Problem Solving
Computer as a tool in solving a variety of mathematical problems.
Possible topics: roots of equations, solutions to differential equations, others.
Introduction to appropriate programming language. Emphasis on graphics.
-Mathematical Modeling
Models and numerical simulations, using differential equations, iterated maps, and probability.
These are most likely the classes I will be taking if I decide to do either a stats or applied math major. I will probably take a couple of programming classes as well.
Also, I plan on double majoring in finance (since my university has a very good b-school)
So.... based on the classes I provided, which would be a better route? Stats or applied math?